Broadcast Communications and Distributed Algorithms

The paper addresses ways in which one can use "broadcast communication" in distributed algorithms and the relevant issues of design and complexity. We present an algorithm for merging k sorted lists of n/k elements using k processors and prove its worst case complexity to be 2n, regardless of the number of processors, while neglecting the cost arising from possible conflicts on the broadcast channel. We also show that this algorithm is optimal under single-channel broadcast communication. In a variation of the algorithm, we show that by using an extra local memory of O(k) the number of broadcasts is reduced to n. When the algorithm is used for sorting n elements with k processors, where each processor sorts its own list first and then merging, it has a complexity of O(n/k log(n/k) + n), and is thus asymptotically optimal for large n. We also discuss the cost incurred by the channel access scheme and prove that resolving conflicts whenever k processors are involved introduces a cost factor of at least log k.